Case-control studies with contaminated controls

This paper considers inference about a parametric binary choice model when the data consist of two distinct samples. The first is a random sample from the people who made choice 1, say, with all relevant covariates completely observed. The second is a random sample from the whole population with only the covariates observed. This is called a contaminated sampling scheme. An example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women, with covariates, whose participant status is unknown. We consider the cases in which the fraction of the population making choice 1 is known and that in which it is not. For both cases we give semiparametrically efficient procedures for estimating the choice model parameters.